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Mathematics · JEE | INTEGRALS

हिन्दी

Match List-I with List-II: List-I List-II A \( \int \tan x \, dx \) I \( \log |\sin x| + C \) B \( \int \cot x \, dx \) II \( \log |\sec x + \tan x| + C \) C \( \int \sec x \, dx \) III \( \log |\sec x| + C \) D \( \int \operatorname{cosec} x \, dx \) IV \( \log |\operatorname{cosec} x - \cot x| + C \) Choose the correct answer from the options given below:

Match List-I with List-II:

List-I List-II
A \( \int \tan x \, dx \) I \( \log |\sin x| + C \)
B \( \int \cot x \, dx \) II \( \log |\sec x + \tan x| + C \)
C \( \int \sec x \, dx \) III \( \log |\sec x| + C \)
D \( \int \operatorname{cosec} x \, dx \) IV \( \log |\operatorname{cosec} x - \cot x| + C \)

Choose the correct answer from the options given below:

  1. A
    A-(IV), B-(II), C-(III), D-(I)
  2. B
    A-(I), B-(III), C-(IV), D-(II)
  3. C
    A-(II), B-(IV), C-(I), D-(III)
  4. D
    A-(III), B-(I), C-(II), D-(IV)
View Answer & Solution

Correct answer · Option D

A-(III), B-(I), C-(II), D-(IV)

Explanation

Standard logarithmic integrations of basic trigonometric functions give \( \int \tan x dx = \log|\sec x|+C \), \( \int \cot x dx = \log|\sin x|+C \), \( \int \sec x dx = \log|\sec x + \tan x|+C \), and \( \int \operatorname{cosec} x dx = \log|\operatorname{cosec} x - \cot x|+C \).
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